PCNN机理研究及其在图像处理中的参数自适应设置
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摘要
PCNN(脉冲耦合神经网络)模型由于其神经元的同步脉冲发放特性和捕获特性,被广泛应用于数字图像分割、边缘检测、噪声滤除、图像增强、检索等处理,成为生物医学影像分析、遥感遥测图像处理、军事目标检测、交通图像处理等领域研究热点。在不断改善PCNN图像处理特性的同时,也存在着一些关键性难点成为国内外研究者共同关注的问题,其中PCNN模型自身数学特性的分析、模型参数的自适应设置对神经元特性的影响等是目前研究的难点和热点。
本文从PCNN模型的系统方程出发,利用数学迭代法和离散系统分析法,对无耦合连接和耦合连接两种状态下的PCNN模型进行神经元点火机理分析,给出神经元点火时刻的数学表达式及其修正公式,同时揭示了PCNN模型本身的数学耦合特性——点火阶梯特性,以及其对网络生物学特性造成的覆盖现象,并对这种现象产生的机理和消除方法进行了分析,在此基础上分析了神经元点火特性受邻域神经元点火状态影响的情况,给出神经元点火时刻提前量数学表达式,进一步提出基于消除PCNN模型数学耦合特性和最大灰度值最小时刻点火两个约束条件的PCNN参数自适应设置方法。在完成神经元点火时刻受网络参数以及邻域神经元点火状态影响规律研究的基础上,本文提出一种PCNN的改进模型,并将其分别用于图像分割和噪声滤波中,同时也提出了一种基于PCNN的图像边缘检测新模型,并针对这三种图像处理,分别进行了参数自适应设置的分析和讨论。论文的主要工作如下：
1.通过对PCNN模型离散方程的数学分析,给出了无耦合连接和耦合连接时神经元点火时刻的数学表达式及其修正公式,揭示了神经元理论点火时刻与实际点火时刻不一致的现象,提出了“数学耦合点火”和“点火阶梯图”的概念,并对神经元点火阶梯特性与网络参数之间的关系进行了详细分析；
2.分别从本神经元点火时刻受点火阶梯的影响以及邻域神经元对本神经元的耦合作用受点火阶梯的影响两个角度,分析了PCNN模型数学耦合特性对网络生物学特性的影响情况,详细讨论了这种干扰和影响产生的机理,提出了消除模型数学耦合特性的参数自适应设置方法,并对算法性能进行了分析；
3.对PCNN模型进行参数的规整,进一步对模型中的调制子系统进行调幅过程的模拟,分析了调制子系统参数设置对网络脉冲发放特性的影响情况,提出了一种具有“精细”脉冲发放特性的改进PCNN模型,并对改进模型的特性进行了分析,提出了参数自适应设置的方法；
4.将上面提出的具有“精细”脉冲发放特性的改进PCNN模型应用于图像分割和噪声滤波中,针对于不同的应用完成了参数自适应设置的讨论,同时也提出了一种基于PCNN的图像边缘检测新模型,并给出了参数自适应设置的方法。
With features of neuron synchronous pulse burst and capture, the Pulse Coupled Neural Network (PCNN) model has been widely applied in processing areas like digital image segmentation, edge detection, noise filtering, image enhancement, retrieval etc. and it has been the hot research area in the field of biomedical image analysis, remote sensing image processing, military target detection and traffic image processing. Yet features of PCNN image processing have been improved continually, there are still some key technical difficulties that has roused attentions from researchers home and abroad. Difficulties like mathematical properties of PCNN model itself and effects of parameters adaptive setting of the model on neuron have become the difficult and hot research subject.
Guided by the system equation of PCNN model and by using mathematical iteration method and the discrete system analysis method neuron firing mechanism of PCNN model was analyzed under two kinds of state, coupling and without coupling. This paper presented the mathematical expression and modifier formula of neuron firing time, revealed the mathematical coupling feature of PCNN model itself, the step firing and the coverage influence it had on the biological characteristics of PCNN. The mechanism caused by that phenomenon as well as ways to eliminate have been analyzed. And based on what have been researched, this paper analyzed the situation that the neuron firing was influenced by the status of neighborhood neuron firing, brought out the mathematical expression of the lead of neuron firing timing and further put out the parameter adaptive setting method of PCNN based on the idea of eliminating the mathematical coupling feature of PCNN model and with two restrictions:the max gray and the minimum time firing. Based on the study of the law that neuron firing time is affected by network parameters and neighborhood neuron firing status, the writer presented an improved PCNN model and applied it into areas like image segmentation and noise filtering and a new model based on image edge detection of PCNN was also presented. In terms of those three ways of image processing, parameters adaptive setting of them have been analyzed and discussed separately. The main work as follows:
1. By mathematical analysis of the discrete equation of PCNN model, the mathematical expression and modifier formula of neuron firing time under two kinds of state, coupling and without coupling were given. The research revealed the phenomenon that the theoretic neuron firing time disaccord with the actual neuron firing time, put out concepts of "mathematics firing" and "diagram of step firing". The relationship between step features of neuron firing and network parameter was analyzed in detail.
2. From perspectives that neuron firing time itself as well as effects of neighborhood neuron on coupling effect of neuron themselves are influenced by firing step, the writer analyzed effects of the mathematical coupling feature of the PCNN model on the feature of network biology, discussed the mechanism caused by interference and influence in detail, put out the parameter adaptive setting method based on the idea of eliminating the mathematical coupling feature of PCNN model and the algorithm performance was analyzed too.
3. Parameters of PCNN model was put in order and simulation for the process of modulation of subsystem of the model was analyzed and from which the information that how did parameters determination of the subsystem influence network pulse burst feature was given. Then an improved PCNN model with a "fine" pulse burst feature was put forward. Features of the improved model were analyzed and parameter adaptive setting method was provided.
4. By applying the improved PCNN model with a "fine" pulse burst feature, mentioned above, into areas of image segmentation and noise filtering, parameters adaptive setting in different applications were discussed and a new image edge detection model based on PCNN as well as parameters adaptive setting methods were put out.
本文从PCNN模型的系统方程出发,利用数学迭代法和离散系统分析法,对无耦合连接和耦合连接两种状态下的PCNN模型进行神经元点火机理分析,给出神经元点火时刻的数学表达式及其修正公式,同时揭示了PCNN模型本身的数学耦合特性——点火阶梯特性,以及其对网络生物学特性造成的覆盖现象,并对这种现象产生的机理和消除方法进行了分析,在此基础上分析了神经元点火特性受邻域神经元点火状态影响的情况,给出神经元点火时刻提前量数学表达式,进一步提出基于消除PCNN模型数学耦合特性和最大灰度值最小时刻点火两个约束条件的PCNN参数自适应设置方法。在完成神经元点火时刻受网络参数以及邻域神经元点火状态影响规律研究的基础上,本文提出一种PCNN的改进模型,并将其分别用于图像分割和噪声滤波中,同时也提出了一种基于PCNN的图像边缘检测新模型,并针对这三种图像处理,分别进行了参数自适应设置的分析和讨论。论文的主要工作如下：
1.通过对PCNN模型离散方程的数学分析,给出了无耦合连接和耦合连接时神经元点火时刻的数学表达式及其修正公式,揭示了神经元理论点火时刻与实际点火时刻不一致的现象,提出了“数学耦合点火”和“点火阶梯图”的概念,并对神经元点火阶梯特性与网络参数之间的关系进行了详细分析；
2.分别从本神经元点火时刻受点火阶梯的影响以及邻域神经元对本神经元的耦合作用受点火阶梯的影响两个角度,分析了PCNN模型数学耦合特性对网络生物学特性的影响情况,详细讨论了这种干扰和影响产生的机理,提出了消除模型数学耦合特性的参数自适应设置方法,并对算法性能进行了分析；
3.对PCNN模型进行参数的规整,进一步对模型中的调制子系统进行调幅过程的模拟,分析了调制子系统参数设置对网络脉冲发放特性的影响情况,提出了一种具有“精细”脉冲发放特性的改进PCNN模型,并对改进模型的特性进行了分析,提出了参数自适应设置的方法；
4.将上面提出的具有“精细”脉冲发放特性的改进PCNN模型应用于图像分割和噪声滤波中,针对于不同的应用完成了参数自适应设置的讨论,同时也提出了一种基于PCNN的图像边缘检测新模型,并给出了参数自适应设置的方法。
With features of neuron synchronous pulse burst and capture, the Pulse Coupled Neural Network (PCNN) model has been widely applied in processing areas like digital image segmentation, edge detection, noise filtering, image enhancement, retrieval etc. and it has been the hot research area in the field of biomedical image analysis, remote sensing image processing, military target detection and traffic image processing. Yet features of PCNN image processing have been improved continually, there are still some key technical difficulties that has roused attentions from researchers home and abroad. Difficulties like mathematical properties of PCNN model itself and effects of parameters adaptive setting of the model on neuron have become the difficult and hot research subject.
Guided by the system equation of PCNN model and by using mathematical iteration method and the discrete system analysis method neuron firing mechanism of PCNN model was analyzed under two kinds of state, coupling and without coupling. This paper presented the mathematical expression and modifier formula of neuron firing time, revealed the mathematical coupling feature of PCNN model itself, the step firing and the coverage influence it had on the biological characteristics of PCNN. The mechanism caused by that phenomenon as well as ways to eliminate have been analyzed. And based on what have been researched, this paper analyzed the situation that the neuron firing was influenced by the status of neighborhood neuron firing, brought out the mathematical expression of the lead of neuron firing timing and further put out the parameter adaptive setting method of PCNN based on the idea of eliminating the mathematical coupling feature of PCNN model and with two restrictions:the max gray and the minimum time firing. Based on the study of the law that neuron firing time is affected by network parameters and neighborhood neuron firing status, the writer presented an improved PCNN model and applied it into areas like image segmentation and noise filtering and a new model based on image edge detection of PCNN was also presented. In terms of those three ways of image processing, parameters adaptive setting of them have been analyzed and discussed separately. The main work as follows:
1. By mathematical analysis of the discrete equation of PCNN model, the mathematical expression and modifier formula of neuron firing time under two kinds of state, coupling and without coupling were given. The research revealed the phenomenon that the theoretic neuron firing time disaccord with the actual neuron firing time, put out concepts of "mathematics firing" and "diagram of step firing". The relationship between step features of neuron firing and network parameter was analyzed in detail.
2. From perspectives that neuron firing time itself as well as effects of neighborhood neuron on coupling effect of neuron themselves are influenced by firing step, the writer analyzed effects of the mathematical coupling feature of the PCNN model on the feature of network biology, discussed the mechanism caused by interference and influence in detail, put out the parameter adaptive setting method based on the idea of eliminating the mathematical coupling feature of PCNN model and the algorithm performance was analyzed too.
3. Parameters of PCNN model was put in order and simulation for the process of modulation of subsystem of the model was analyzed and from which the information that how did parameters determination of the subsystem influence network pulse burst feature was given. Then an improved PCNN model with a "fine" pulse burst feature was put forward. Features of the improved model were analyzed and parameter adaptive setting method was provided.
4. By applying the improved PCNN model with a "fine" pulse burst feature, mentioned above, into areas of image segmentation and noise filtering, parameters adaptive setting in different applications were discussed and a new image edge detection model based on PCNN as well as parameters adaptive setting methods were put out.
引文
[1]Eckhorn, R., Reitboeck, H.J., Arndt, M., Dicke, P. Feature linking via synchronization among distributed assemblies:simulation of results from cat visual cortex[J]. Neural Computation. 1990,2(3):293-307.
[2]Johnson, J.L., Padgett, M.L. PCNN models and applications[J]. IEEE Trans. on Neural Networks.1999,10(3):480-498.
[3]马义德,李廉,绽琨.王兆斌.脉冲耦合神经网络与数字图像处理[M].科学出版社.2008.
[4]Eckhorn, R., Frien, A., Bauer, R., et al. High frequency oscillations in primary visual cortex of awake monkey[J]. NeuroReport.1993,4(3):243-246.
[5]Johnson, J.L., Ritter, D. Observation of periodic waves in a pulse-coupled neural network[J]. Optics letters,1993,18(15):1253-1255.
[6]张军英,樊秀菊,董继扬.一种改进型脉冲耦合神经网络及其图像分割[J].电子学报.2004,32(7)：1223-1226.
[7]Yun feng, Miao Jun, Duan Lijuan, et al. A new approach to image segmentation based on simplified region growing PCNN[J].Applied Mathematics and Compution.2008,205(2): 807-814.
[8]Jiesheng Wang, Fengwu Cong. Grayscale image edge detection based on pulse-coupled neural network and particle swarm optimization[C].2008 Chinese Control and Decision Conference. 2008,2576-2579.
[9]Zhang Jiuwen.,Zhan Kun.,Ma Yide.Rotation and scale invariant antinoise PCNN features for content based image retrieval[J]. Neural Network World.2007,2:121-132.
[10]石美红,张军英,李永刚.一种新的低对比度图像增强的方法术[J].计算机应用研究.2005,1：235-238.
[11]Broussard, R.P., Rogers, S.K., Oxley, M.E., et al. Physiologically motivated image fusion for object detection using a pulse coupled neural network[J]. IEEE Trans. on Neural Networks. 1999,10(3):554-563.
[12]Shang, L., Yi, Z. A class of binary images thinning using two PCNNs[J]. Neurocomputing. 2006,7:1-13.
[13]Li, W., Zhu, X. A new image fusion algorithm based on wavelet packet analysis and PCNN[C]. Proc. of the 4th International Conference on Machine Learning and Cybernetics. 2005,9:5297-5301.
[14]Godin, C., Muller, J.D., et al. Pattern recognition with spiking neurons:performance enhancement based on a statistical analysis[C]. Neural Networks.1999, IJCNN'99. International Joint Conference on. IEEE,1999,3:1876-1880.
[15]Wang, Z., Ma, Y., Xu, G. A new approach to iris recognition[C]. International Journal of Information Acquisition.2007,4 (1):69-76.
[16]Muresan, R.C. Pattern recognition using pulse-coupled neural networks and discrete Fourier transforms[J]. Neurocomputing.2003,51:478-493.
[17]Ranganath, H.S., Kuntimad, G. Object detection using pulse coupled neural networks[J]. IEEE Trans, on Neural Networks.1999,10(3):615-620.
[18]Qing L, Yide M, et al. Image target recognition using pulse coupled neural networks time matrix[C]//Control Conference,2007. CCC 2007. Chinese. IEEE,2007:96-99.
[19]Ji., L., Yi, Z. A mixed noise image filtering method using weighted-linking PCNNs[J]. Neurocomputing.2008,71(13):2986-3000.
[20]Shi, M.H., Zhang, J.Y., Zhu, X.J,.Zhang, X.B. A method of image gauss noise filtering based on PCNN[J]. Computer Applications.2002,22(6):177-183.
[21]石美红,张军英,朱欣娟.基于PCNN的图像高斯噪声滤波的方法[J].计算机应用.2002,22(6)：1-4.
[22]马义德,史飞,李廉等.一种基于脉冲耦合神经网络的脉冲噪声滤波器设计[J].生物医学工程学杂志.2004,21(6)：1019-1023.
[23]Russo, F. A method for estimation and filtering of Gaussian noise in images[J]. IEEE Trans. Instrum. Meas.2003,52(4):1148-1154.
[24]李永刚,石美红,魏远旺.基于PCNN图像高斯噪声滤波[J].计算机工程与应用.2007,43(1)：65-67.
[25]Cai, G, Li, H., Xu, D., et al. Impulse noise filtering by using an adaptive single-linking pulse coupled neural network[C]//Software Engineering and Service Sciences (ICSESS),2010 IEEE International Conference on. IEEE,2010,07-110.
[26]Wang, W., Li, M., Liu, G. New color image filtering algorithm based on PCNN [J]. Computer Engineering and Design.2007,14:042.
[27]Yu, B., Zhang, L. Pulse coupled neural network for motion detection[C]. Neural Networks, 2003. Proceedings of the International Joint Conference on, IEEE.2003,2:1179-1184.
[28]赵荣昌,马义德,绽琨.三态层叠PCNN原理及在最短路径求解中的应用[J].系统工程与电子技术.2008,30(9)：1785-1789.
[29]马义德,张红娟.PCNN与灰度形态学相结合的图像去噪方法[J].北京邮电大学学报.2008,31(2)：108-112.
[30]马义德,李廉,戴若兰.一种基于脉冲耦合神经网络的植物胚胎细胞图像的分割研究[J].科学通报,2001,46(21)：1781-1787.
[31]Zhang, Y, Wu, L. Pattern recognition via PCNN and Tsallis entropy[J]. Sensors.2008,8(11): 7518-7529.
[32]Muresan, R.C. Pattern recognition using pulse-coupled neural networks and discrete Fourier transforms[J]. Neurocomputing.2003,51:487-493.
[33]Wei, Z.Q., Xue, X., Yin, B., et al. AUV sonar image processing based on improved pulse coupled neural network model and morphology[C]. Control and Automation (ICCA),2010 8th IEEE International Conference on. IEEE.2010:365-369.
[34]Karvonen, J.A. Baltic sea ice SAR segmentation and classification using modified pulse-coupled neural networks[J]. Geoscience and Remote Sensing, IEEE Transactions on. 2004,42(7):1566-1574.
[35]Chacon, M., Zimmerman, S. License plate location based on a dynamic PCNN scheme[C]. Neural Networks,2003. Proceedings of the International Joint Conference on. IEEE.2003,2: 1195-1200.
[36]张平均;基于PCNN的智能交通系统路径优化技术研究[硕士论文];重庆：重庆大学：2003.
[37]姚畅,陈后金,李居朋.改进型脉冲耦合神经网络在图像处理中的动态行为分析[J].自动化学报,2008,34(10)：1291-1297.
[38]Zhang, J., Dong, J., Shi, M. An adaptive method for image filtering with pulse-coupled neural networks[C]. Proc. of International Conference on Image processing.2005,2:Ⅱ-133-6
[39]Berg, H., Olsson, R., Lindblad, T., et al. Automatic design of pulse coupled neurons for image segmentation[J]. Neurocomputing.2008,71(10):1980-1993.
[40]Gu, X., Guo, S., Yu, D. A new approach for automated image segmentation based on unit-linking PCNN[C]. Proceedings of the First International Conference on Machine Learning and Cybemetics.2002,175-177.
[41]Wang Zhaobin, Ma Yide, Cheng Feiyan, et al. Review of pulse-coupled neural networks[J]. Image and Vision Computing,2010,28(1):5-13.
[42]Zhao, Z., Zhao, C., Zhang, Z.H. A new method of PCNN's parameter's optimization[J]. Dianzi Xuebao(Acta Electronica Sinica).2007,35(5):996-1000.
[43]Russo, F. Technique for image denoising based on adaptive piecewise linear filters and automatic parameter tuning[J]. IEEE Trans. Instrum. Meas.2006,55 (4):1362-1367.
[44]马义德,戴若兰,李廉.一种基于脉冲耦合神经网络和图像熵的自动图像分割方法[J].通信学报.2002,23(1)：46-51.
[45]Broussard, R.P. Physiologically-based vision modeling applications and gradient descent-based parameter adaptation of pulse coupled neural networks[R]. Air Force Inst Of Tech Wright-Patterson Afb Oh.1 997.
[46]赵峙江,赵春晖,张志宏.一种新的PCNN模型参数估算方法[J].电子学报,2007,35(5)：996-1000.
[47]Kuntimad, G., Ranganath, H.S. Perfect image segmentation using pulse coupled neural networks[J]. IEEE Trans. Neural Networks.1999,10(3):591-598.
[48]于江波,陈后金,王巍等.脉冲耦合神经网络在图像处理中的参数确定[J].电子学报,2008,36(1)：81-85.
[49]Li Min, Cai Wei, Tan Zheng. Adaptive parameters determination method of pulse coupled neural network based on water valley area[C]. Neural Information Processing pt.2. Hong Kong,2006,713-720.
[50]马义德,齐春亮.基于遗传算法的脉冲耦合神经网络自动系统的研究[J].系统仿真学报,2006,18(03)：722-724.
[51]Chen Yuli, Park Sung-Kee, Ma Yide. A new automatic parameter setting method of a simplified PCNN for image segmentation[J]. IEEE Transactions on Neural Networks.2011, 22 (6):880-892.
[52]Yong Li, Ke Wang, Da-ke Chen. Multispectral and Panchromatic Images Fusion by Adaptive PCNN[C].16th International Multimedia Modeling Conference. Chongqing,2010, 120-129..
[53]Zhou Liang, Sun Yu, Zheng Jianguo. Automated color image edge detection using improved PCNN model[J]. WSEAS Transactions on Computers.2008,17(4):184-189.
[54]刘远民,秦世引.一种新的基于PCNN的自适应强去噪方法[J].北京航空航天大学学 报.2009,35(1)：108-112.
[55]Ota,Y, VLSI structure for static image processing with pulse-coupled neural network[C]. IECON 02 [Industrial Electronics Society, IEEE 2002 28th Annual Conference of the]. IEEE. 2002,4:3221-3226.
[56]Gu, X., Zhang, L. Morphology open operation in unit-linking pulse coupled neural network for image processing[C]. Proc. of International Conference on signal processing.2005,2: 1597-1600.
[57]Zhang, X., Minai, A.A. Detecting corresponding segments across images using synchronizable Pulse-Coupled neural networks[C]. Neural Networks,2001. Proceedings. IJCNN'01. International Joint Conference on. IEEE.2001,2:820-825.
[58]Stewart, R.D., Fermin, I., Opper, M. Region growing with pulse-coupled neural networks:an alternative to seeded region growing[J]. IEEE Neural Networks.2002,13(6):1577-1662.
[59]Chacon, M.M.I., Zimmerman, A.S. Image processing using the PCNN time matrix as a selective filter[C]//Image Proceedings,2003. ICIP 2003. Proceedings.2003 International Conference on. IEEE.2003,1(1):Ⅰ-877-80.
[60]Qu, H., Yi, Z. A new algorithm for finding the shortest paths using PCNNs[J]. Chaos, Solitons & Fractals.2007,33(4):1220-1229.
[61]Wang, Z., Ma, Y, Gu, J. Multi-focus image fusion using PCNN[J]. Pattern Recognition.2010, 43(6):2003-2016.
[62]Lindblad, T., Kinser, J.M. Image processing using pulse-coupled neural networks[M]. Springer.2005.
[63]Shang, L., Zhang, Y. A class of binary images thinning using two PCNNs[J]. Neurocomputing.2007,70 (4-6):1096-1101.
[64]Gu, X.D., Cheng, C.Q., Yu, D.H. Noise-reducing of four-level image using PCNN and fuzzy algorithm[J]. Journal of Electronics and Information Technology.2003,25(12):1585.
[65]毕英伟,邱天爽.一种基于简化PCNN的自适应图像分割方法[J].电子学报,2005,33(4)：647-650.
[66]Berg, H., Olsson, R., Lindblad, T., Chilo, J. Automatic design of pulse coupled neurons for image segmentation[J]. Neurocomputing.2008,71(10-12):1980-1993.
[67]Wei, S., Hong, Q., Hou, M. Automatic image segmentation based on PCNN with adaptive threshold time constant[J]. Neurocomputing.2011,74(9):1485-1491.
[68]Weber, E.H., De pulsu, resorptione, auditu et tactu. annotationes anatomicae et physiologicae. Leipzig, Germany:C.F. Kohler,1834.
[69]Fechner, G.T., Elemente der pshchophysik. Leipzig, Germany:Breitkopf & Hartel,1860.
[70]Broussard, R.P., Rogers, S.K., Oxley, M.E., et al. Physiologically motivated image fusion for object detection using a pulse coupled neural network[J]. IEEE Transactions on Neural Networks.1999,10(3):554-563.
[71]Ranganath, H.S., Kuntimad G.J., Johnson, L. Pulse coupled neural networks for image processing[J]. IEEE Southeastcon, Raleigh, NC.1995,37-43.
[72]Ranganath, H.S., Kuntimad, G. Object detection using pulse coupled neural networks[J]. IEEE Transactions on Neural Networks.1999,10(3):615-620.
[73]顾晓东;郭仕德;余道衡.一种用PCNN进行图像边缘检测的新方法.计算机工程与应 用,2003.39(16)：1-2,55.
[74]Kang Chungchia, Wang Wenjune. A novel edge detection method based on the maximizing objective function[J]. Pattern Recognition.2007,40(2):609-618.
[75]Zhang, J., Lu, Z., Shi, L., et al. Filtering images contaminated with pep and salt type noise with pulse-coupled neural networks[J]. Science in China Series F:Information Sciences. 2005,48(3):322-334.
[76]Wang, Z.., Ma, Y., Xu, G. A novel method of iris feature extraction based on the ICM[C]. Proc. of the International Conference on Information Acquisition.2006,814-818.
[77]Bouzouba, K., Radouane, L. Image identification and estimation using the maximum entropy principle[J]. Pattern Recognition Letters.2000,21(8):691-700.
[78]Ma, Y., Wang, Zhaobin, Wu, C. Feature extraction from noisy image using PCNN[C]. Proc. of the International Conference on Information Acquisition.2006,808-813.
[79]Ma, Y., Lin, D., Zhang, B., et al. A novel algorithm of image enhancement based on pulse coupled neural network time matrix and rough set[C]. Fuzzy Systems and Knowledge Discovery,2007. FSKD 2007. Fourth International Conference on. IEEE.2007,3:86-90.
[80]Vega-pineda, J., Chacon-Murguia, M.I., Camarillo-Cisneros, R. Synthesis of pulse-coupled neural networks in FPGAs for real-time image segmentation[C]. Proc. of International Joint Conference on Neural Networks.2006,4051-4055.
[81]Kinser, J.M., Lindblad, T. Implementation of pulse-coupled neural networks in a CNAPS environment[J]. Neural Networks, IEEE Transactions on.1999,10(3):584-590.
[82]Forgac, R., Mokris, I. Feature generation improving by optimized PCNN[C]. Proc. Of 6th International Symposium on Applied Machine Intelligence and Informatics.2008,203-207.
[83]Johnson, J.L. Pulse-coupled neural nets:translation, rotation, scale and intensity signal invariances for image [J]. Applied Optics.1994,33(26):6239-6253.
[84]Yide, M., Qing, L., Zhibai, Q. Automated image segmentation using improved PCNN model based on cross-entropy[C]. Intelligent Multimedia, Video and Speech Processing,2004. Proceedings of 2004 International Symposium on. IEEE.2004:743-746.
[85]章毓晋.图像分割[M].科学出版社.2001.
[86]Otsu, N. A threshold selection method from gray-level histograms[J]. Automatica.1975, 11(285-296):23-27.
[87]Felzenszwalb, P.F., Huttenlocher, D.P. Efficient graph-based image segmentation[J]. International Journal of Computer Vision.2004,59(2):167-181.
[88]Zhang, Y.J. A review of recent evaluation methods for image segmentation[C]. Signal Processing and its Applications, Sixth International, Symposium on.2001. IEEE.2001,1: 148-151.
[89]马义德,钱志柏.基于聚类算法的图像分割技术[J].中国科技论文在线,2004,03,18.
[90]钱志柏.基于模糊聚类和PCNN的图像分割新算法研究[硕士论文].兰州：兰州大学.2004.
[91]Mario, F., Giuseppe, B., Terry, C. Entropy-based representation of image information[J]. Pattern Recognition Letters.2002,23(12):1391-1398.
[92]Kanungo, T., Mount, D.M., et al. An efficient k-means clustering algorithm:analysis and implementation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002, 24(7):881-892.
[93]Wu, H.S., Barba, J., Gil, J. A parametric fitting algorithm for segmentation of cell images[J]. IEEE Transactions on Biomedical Engineering.1998,45(3):400-407.
[94]黄凤岗,杨国,宋克鸥.柔性(soft)形态学在图像边缘检测中的应用[J].中国图象图形学报,2000,5(4)：284-287.
[95]杨文杰,刘浩学,马昆.边界探测的小波变换方法[J].中国图象图形学报.1999,4(1)：38-40.
[96]王浩军,毛柏鑫,笃彦等.原位分子杂交图像中银粒的分割[J].中国图象图形报.1999,4(6)：454-457.
[97]耿伯英,杨静宇.一种基于一致性邻域超图模型的图像分割[J].中国图象图形学报,2000,5(4)：288-292.
[98]魏志成,周激流,吕航等.一种新的图像分割自适应算法的研究[J].中国图象图形学报.2000,5(3)：217-220.
[99]Kurugollu, F., Sankur, B., Emre Harmanci A. Image segmentation by relaxation using constraint satisfaction neural network[J]. Image and Vision Computing.2002,20(7): 483-497.
[100]Chang, C.L., Ching, Y.T. Fuzzy Hopfield neural network with fixed weight for medical image segmentation[J]. Optical Engineering.2002,41(2):351-358.
[101]Skourikhine, A.N. Pulse couple neural network for image smoothing and Segmentation[A]. International Symposium on Computational Intelligence[C]. Kosice, Slovakia,2000.
[102]Ma Yide, Dai Rolan, Li Lian, et al. Image segmentation of embryonic plant cell using pulse-coupled neural networks[J]. Chinese Science Bulletion.2002,47(02):167-172.
[103]刘勃,马义德.一种基于交叉熵改进型PCNN图像自动分割新方法[J].中国图象图形学报.2005,10(5)：579-584.
[104]Spreeuwers, L.J. Neural network edge detector[C]. Electronic Imaging'91, San Jose, CA. International Society for Optics and Photonics.1991:204-215.
[105]Dhawan, A.P., Dufresene, T. Low-level image processing and edge enhancement using a self-organizing neural network[J]. Proc.IEEE J Conf.on Neural networks.1990:503-510.
[106]邓翔宇,马义德.PCNN参数自适应设定及其模型的改进[J].电子学报.2012,40(5)：955-964.
[107]Ranganath, H. S., Kuntimad, G. Object detection using pulse coupled neural networks [J]. IEEE Transactions on Neural Networks.1999,10(3):615-620.
[108]Gu Xiaodong, Wang Yuanyuan, Zhang Liming. Object detection using unit-linking PCNN image icons [J]. Lecture Notes in Computer Science.2006,3972:616-622.
[109]Yu, B., Zhang, L.. Pulse coupled neural network for motion detection[C]. Proc. of the Joint International Conferences on Neural Networks.2003,1179-1184.
[110]Ekblad, U., Kinser, J.M. Theoretical foundation of the intersecting cortical model and its use for change detection of aircraft, cars, and nuclear explosion tests[J]. Signal Processing.2004, 84(7):1131-1146.
[111]Fabio, Pacifici., Fabio Del Frate. Automatic change detection in very high resolutionlmages with pulse-coupled neural networks[J]. IEEE Geoscience and Remote Sensing Letters.2010, 7(1):58-62.
[112]Hongzhao Y., Guifa H., Yong L. Pulse Coupled Neural Network Algorithm for Object Detection in Infrared Image[C]. Computer Network and Multimedia Technology.2009, CNMT 2009. International Symposium on. IEEE,2009:1-4.
[113]宋寅卯,袁端磊,卢易枫等.基于最优PCNN模型的织物疵点白动检测[J].仪器仪表学报,2008,29(4)：888-891.
[114]刘勃,许录平,马义德等.结合灰度嫡变换的PCNN小目标图像检测新方法[J].北京理工大学学报.2009,29(12)：1085-1090.
[115]Chen Qiuhong, Zhou Liang. A pulse-coupled neural network for color image edge detection[C]. Proceedings of the 8th WSEAS International Conference on Applied Computer and Applied Computational Science.2009,441-445.
[116]Bellon, O., Silva, L. New improvements to range image segmentation by edge detection. IEEE Signal Process Letters.2002,9 (2):43-45.
[117]Arbelaez, P., Maire, M., Fowlkes, C. et al. Contour detection and hierarchical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence.2010,33(5): 898-916.
[118]Spacek, A.. Edge detection and motion detection. Image and vision computing.1986,4(1): 43-56.
[119]Yongsheng Gao, M. K. H. Leung. Face recognition using line edge map. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002,24(6):764-79.
[120]Qiuying Yang., Xingyuan Gao. Tracking on motion of small target based on edge detection. In:Proceedings of 2009 WRI World Congress on Computer Science and Information Engineering, Los Angeles, CA, USA.2009,6:619-622.
[121]史飞.脉冲耦合神经网络在图像处理中的应用研究[硕士论文].兰州：兰州大学.2003.
[122]马义德,张祥光.非线性滤波器除噪技术综述[J].中国科技论文在线.2004.
[123]张兆礼,赵春晖,梅晓丹.现代图像处理技术及MATLAB实现[M].北京：人民邮电出版社.2001.
[124]Brownrigg, D.R.K. The weighted median filter[J]. Communications of the ACM.1984, 27(8):807-818.
[125]阮秋琦.数字图像处理学[M].北京：电子工业出版社.2001.
[126]Ko, S.J., Lee, Y.H. Center weighted median filger and their application to image enhancement[J]. IEEE Trans. On Circ. Syst.1991,38:984-993.
[127]梁雯,刘松林.图像中心加权中值滤波的改进与应用[J].中国图象图形学报.1997,2(8,9)：629-632.
[128]冯星奎,肖兴明,尹洪君.方向加权中值滤波算法[J].中国图象图形学报.2000,5(7)：609-611.
[129]Sun, T., Neuvo, Y. Detail-preserving median based filters in image processing[J]. Pattern Recognition Letters.1994,15(4):341-347.
[130]Yang Ruikang. Optimal weighted median filtering under structural constrains[J]. IEEE Transactions on Signal Processing.1995,43(3):591-603.
[131]常瑞娜,穆晓敏,杨守义等.基于局部空间像素特征的白适应加权滤波算法[J].计算机工程与应用.2008,44(6)：45-47.
[132]Eng, H.L., Ma, K.K. Noise adaptive soft-switching median filter[J]. Image Processing, IEEE Transactions on.2001,10(2):242-251.
[133]Brownrigg, D. Decision-based median filter using local signal statistics[C]. Proc.SPIE IntSymp. Visual Communications Image Processing, chicago.1994,2308:268-275.
[134]黄煦涛.二维数字信号处理Ⅱ-变换与中值滤波器[M].北京：科学出版社.1985.
[135]Czerwinski, R.N., Jones, D.L., Brien, W.D. Ultrasound speckle reduction by directional median filtering[A]. Proc.IEEE Int. Conf.Image Processing,Wasington DC, USA.1995, 358-361.
[136]齐春亮,马义德.自适应中值滤波器的实现与在图像降噪中的应用.中国科技论文在线2005,03,15.
[137]蔡汉添.小波变换域中图像噪声平滑技术[J].光学技术,1998,6：6-9.
[138]Donoho, D.L. De-noising by soft-thresholding[J]. IEEE Trans.Inform. Theory.1995,41(3): 613-627.
[139]张久文,马义德.一种基于小波变换的迭代自适应图像除噪算法[J].兰州大学学报.2005,41(2)：74-77.
[140]Sternberg, S.R. Grayscale morphology[J]. Computer Vision,Graphics,and Image Processing. 1986,35(1):333-355.
[141]Sinha, D., Dougherty, E.R. Fuzzy mathematical morphology [J]. Journal of Visual Communication and Image Representation.1992, (3):286-302.
[142]Koskinen, L., Astola J., Neuvo, Y. Soft morphological filters[C]. Proc.SPIE Int.Society of Optical Engineering.1991,1568:262-270.
[143]刘志敏,杨杰.基于数字形态学的图像形态滤波[J].红外与激光工程.1999,28(4)：10-15.
[144]马义德,张祥光,杨淼.基于多结构元广义形态滤波的改进算法[J].电子科技大学学报.2004,33(4)：391-394.
[145]马义德,杨淼,李廉.一种全方位多角度自适应形态滤波器及其算法[J].通信学报.2004,25(9)：86-92.
[146]Yuksel, M.E. A hybrid neuro-fuzzy filter for edge preserving restoration of images corrupted by impulse noise[J]. Image Processing, IEEE Transactions on.2006,15(4):928-936.
[147]Morillas, S., Gregori, V, Peris-Fajarnes, G., et al. Local self-adaptive fuzzy filter for impulsive noise removal in color images[J]. Signal Processing.2008,88(2):390-398.
[148]Chenchen Liu, Zhimeng Zhang. Sonar images de-noising based on pulse coupled neural networks[C].1st International Congress on Image and Signal Processing.2008,403-406.
[149]Yi-de M., Fei, S., Lian, L. Gaussian noise filter based on PCNN[C]. Neural Networks and Signal Processing,2003. Proceedings of the 2003 International Conference on. IEEE.2003, 1:149-151.
[150]Yide Ma, dongmei Lin, Beidou Zhang, et al. A novel algorithm of image Gaussian noise filtering based on PCNN time matrix[C].2007 IEEE international Conference on Signal processing and Communications.2007,1499-1502.
[151]石美红,毛江辉,梁颖等.一种强高斯噪声的图像滤波方法[J].计算机应用.2007,27(7)：1637-1640.
[152]Yongqiu Tu,Shaofa Li, Minqin Wang. Mixed-noise removal for color images using modified PCNN model[C]. Second International Symposium on Intelligent Information Technology Application.2008,347-351.
[153]Zou, B., Zhou, H., Chen, H, et al. Multi-Channel Image Noise Filter based on PCNN[J]. Journal of Computers.2012,7(2):475-482.
[154]Jinping He, Kun Gao, Guoqiang Ni. A novel method of image Gaussian noise filtering based on series connected PCNN model[C].2008 International Conference on Optical instruments and Technology:Optical Systems and Optoelectronic Instruments.2008,16-19.
[155]He, K., Li, S.F, Wang, C. Modified PCNN model and Its application to mixed-noise Removal[C]. Innovative Computing & Communication,2010 Intl Conf on and Information Technology & Ocean Engineering,2010 Asia-Pacific Conf on (CICC-ITOE). IEEE.2010: 213-216.
[2]Johnson, J.L., Padgett, M.L. PCNN models and applications[J]. IEEE Trans. on Neural Networks.1999,10(3):480-498.
[3]马义德,李廉,绽琨.王兆斌.脉冲耦合神经网络与数字图像处理[M].科学出版社.2008.
[4]Eckhorn, R., Frien, A., Bauer, R., et al. High frequency oscillations in primary visual cortex of awake monkey[J]. NeuroReport.1993,4(3):243-246.
[5]Johnson, J.L., Ritter, D. Observation of periodic waves in a pulse-coupled neural network[J]. Optics letters,1993,18(15):1253-1255.
[6]张军英,樊秀菊,董继扬.一种改进型脉冲耦合神经网络及其图像分割[J].电子学报.2004,32(7)：1223-1226.
[7]Yun feng, Miao Jun, Duan Lijuan, et al. A new approach to image segmentation based on simplified region growing PCNN[J].Applied Mathematics and Compution.2008,205(2): 807-814.
[8]Jiesheng Wang, Fengwu Cong. Grayscale image edge detection based on pulse-coupled neural network and particle swarm optimization[C].2008 Chinese Control and Decision Conference. 2008,2576-2579.
[9]Zhang Jiuwen.,Zhan Kun.,Ma Yide.Rotation and scale invariant antinoise PCNN features for content based image retrieval[J]. Neural Network World.2007,2:121-132.
[10]石美红,张军英,李永刚.一种新的低对比度图像增强的方法术[J].计算机应用研究.2005,1：235-238.
[11]Broussard, R.P., Rogers, S.K., Oxley, M.E., et al. Physiologically motivated image fusion for object detection using a pulse coupled neural network[J]. IEEE Trans. on Neural Networks. 1999,10(3):554-563.
[12]Shang, L., Yi, Z. A class of binary images thinning using two PCNNs[J]. Neurocomputing. 2006,7:1-13.
[13]Li, W., Zhu, X. A new image fusion algorithm based on wavelet packet analysis and PCNN[C]. Proc. of the 4th International Conference on Machine Learning and Cybernetics. 2005,9:5297-5301.
[14]Godin, C., Muller, J.D., et al. Pattern recognition with spiking neurons:performance enhancement based on a statistical analysis[C]. Neural Networks.1999, IJCNN'99. International Joint Conference on. IEEE,1999,3:1876-1880.
[15]Wang, Z., Ma, Y., Xu, G. A new approach to iris recognition[C]. International Journal of Information Acquisition.2007,4 (1):69-76.
[16]Muresan, R.C. Pattern recognition using pulse-coupled neural networks and discrete Fourier transforms[J]. Neurocomputing.2003,51:478-493.
[17]Ranganath, H.S., Kuntimad, G. Object detection using pulse coupled neural networks[J]. IEEE Trans, on Neural Networks.1999,10(3):615-620.
[18]Qing L, Yide M, et al. Image target recognition using pulse coupled neural networks time matrix[C]//Control Conference,2007. CCC 2007. Chinese. IEEE,2007:96-99.
[19]Ji., L., Yi, Z. A mixed noise image filtering method using weighted-linking PCNNs[J]. Neurocomputing.2008,71(13):2986-3000.
[20]Shi, M.H., Zhang, J.Y., Zhu, X.J,.Zhang, X.B. A method of image gauss noise filtering based on PCNN[J]. Computer Applications.2002,22(6):177-183.
[21]石美红,张军英,朱欣娟.基于PCNN的图像高斯噪声滤波的方法[J].计算机应用.2002,22(6)：1-4.
[22]马义德,史飞,李廉等.一种基于脉冲耦合神经网络的脉冲噪声滤波器设计[J].生物医学工程学杂志.2004,21(6)：1019-1023.
[23]Russo, F. A method for estimation and filtering of Gaussian noise in images[J]. IEEE Trans. Instrum. Meas.2003,52(4):1148-1154.
[24]李永刚,石美红,魏远旺.基于PCNN图像高斯噪声滤波[J].计算机工程与应用.2007,43(1)：65-67.
[25]Cai, G, Li, H., Xu, D., et al. Impulse noise filtering by using an adaptive single-linking pulse coupled neural network[C]//Software Engineering and Service Sciences (ICSESS),2010 IEEE International Conference on. IEEE,2010,07-110.
[26]Wang, W., Li, M., Liu, G. New color image filtering algorithm based on PCNN [J]. Computer Engineering and Design.2007,14:042.
[27]Yu, B., Zhang, L. Pulse coupled neural network for motion detection[C]. Neural Networks, 2003. Proceedings of the International Joint Conference on, IEEE.2003,2:1179-1184.
[28]赵荣昌,马义德,绽琨.三态层叠PCNN原理及在最短路径求解中的应用[J].系统工程与电子技术.2008,30(9)：1785-1789.
[29]马义德,张红娟.PCNN与灰度形态学相结合的图像去噪方法[J].北京邮电大学学报.2008,31(2)：108-112.
[30]马义德,李廉,戴若兰.一种基于脉冲耦合神经网络的植物胚胎细胞图像的分割研究[J].科学通报,2001,46(21)：1781-1787.
[31]Zhang, Y, Wu, L. Pattern recognition via PCNN and Tsallis entropy[J]. Sensors.2008,8(11): 7518-7529.
[32]Muresan, R.C. Pattern recognition using pulse-coupled neural networks and discrete Fourier transforms[J]. Neurocomputing.2003,51:487-493.
[33]Wei, Z.Q., Xue, X., Yin, B., et al. AUV sonar image processing based on improved pulse coupled neural network model and morphology[C]. Control and Automation (ICCA),2010 8th IEEE International Conference on. IEEE.2010:365-369.
[34]Karvonen, J.A. Baltic sea ice SAR segmentation and classification using modified pulse-coupled neural networks[J]. Geoscience and Remote Sensing, IEEE Transactions on. 2004,42(7):1566-1574.
[35]Chacon, M., Zimmerman, S. License plate location based on a dynamic PCNN scheme[C]. Neural Networks,2003. Proceedings of the International Joint Conference on. IEEE.2003,2: 1195-1200.
[36]张平均;基于PCNN的智能交通系统路径优化技术研究[硕士论文];重庆：重庆大学：2003.
[37]姚畅,陈后金,李居朋.改进型脉冲耦合神经网络在图像处理中的动态行为分析[J].自动化学报,2008,34(10)：1291-1297.
[38]Zhang, J., Dong, J., Shi, M. An adaptive method for image filtering with pulse-coupled neural networks[C]. Proc. of International Conference on Image processing.2005,2:Ⅱ-133-6
[39]Berg, H., Olsson, R., Lindblad, T., et al. Automatic design of pulse coupled neurons for image segmentation[J]. Neurocomputing.2008,71(10):1980-1993.
[40]Gu, X., Guo, S., Yu, D. A new approach for automated image segmentation based on unit-linking PCNN[C]. Proceedings of the First International Conference on Machine Learning and Cybemetics.2002,175-177.
[41]Wang Zhaobin, Ma Yide, Cheng Feiyan, et al. Review of pulse-coupled neural networks[J]. Image and Vision Computing,2010,28(1):5-13.
[42]Zhao, Z., Zhao, C., Zhang, Z.H. A new method of PCNN's parameter's optimization[J]. Dianzi Xuebao(Acta Electronica Sinica).2007,35(5):996-1000.
[43]Russo, F. Technique for image denoising based on adaptive piecewise linear filters and automatic parameter tuning[J]. IEEE Trans. Instrum. Meas.2006,55 (4):1362-1367.
[44]马义德,戴若兰,李廉.一种基于脉冲耦合神经网络和图像熵的自动图像分割方法[J].通信学报.2002,23(1)：46-51.
[45]Broussard, R.P. Physiologically-based vision modeling applications and gradient descent-based parameter adaptation of pulse coupled neural networks[R]. Air Force Inst Of Tech Wright-Patterson Afb Oh.1 997.
[46]赵峙江,赵春晖,张志宏.一种新的PCNN模型参数估算方法[J].电子学报,2007,35(5)：996-1000.
[47]Kuntimad, G., Ranganath, H.S. Perfect image segmentation using pulse coupled neural networks[J]. IEEE Trans. Neural Networks.1999,10(3):591-598.
[48]于江波,陈后金,王巍等.脉冲耦合神经网络在图像处理中的参数确定[J].电子学报,2008,36(1)：81-85.
[49]Li Min, Cai Wei, Tan Zheng. Adaptive parameters determination method of pulse coupled neural network based on water valley area[C]. Neural Information Processing pt.2. Hong Kong,2006,713-720.
[50]马义德,齐春亮.基于遗传算法的脉冲耦合神经网络自动系统的研究[J].系统仿真学报,2006,18(03)：722-724.
[51]Chen Yuli, Park Sung-Kee, Ma Yide. A new automatic parameter setting method of a simplified PCNN for image segmentation[J]. IEEE Transactions on Neural Networks.2011, 22 (6):880-892.
[52]Yong Li, Ke Wang, Da-ke Chen. Multispectral and Panchromatic Images Fusion by Adaptive PCNN[C].16th International Multimedia Modeling Conference. Chongqing,2010, 120-129..
[53]Zhou Liang, Sun Yu, Zheng Jianguo. Automated color image edge detection using improved PCNN model[J]. WSEAS Transactions on Computers.2008,17(4):184-189.
[54]刘远民,秦世引.一种新的基于PCNN的自适应强去噪方法[J].北京航空航天大学学 报.2009,35(1)：108-112.
[55]Ota,Y, VLSI structure for static image processing with pulse-coupled neural network[C]. IECON 02 [Industrial Electronics Society, IEEE 2002 28th Annual Conference of the]. IEEE. 2002,4:3221-3226.
[56]Gu, X., Zhang, L. Morphology open operation in unit-linking pulse coupled neural network for image processing[C]. Proc. of International Conference on signal processing.2005,2: 1597-1600.
[57]Zhang, X., Minai, A.A. Detecting corresponding segments across images using synchronizable Pulse-Coupled neural networks[C]. Neural Networks,2001. Proceedings. IJCNN'01. International Joint Conference on. IEEE.2001,2:820-825.
[58]Stewart, R.D., Fermin, I., Opper, M. Region growing with pulse-coupled neural networks:an alternative to seeded region growing[J]. IEEE Neural Networks.2002,13(6):1577-1662.
[59]Chacon, M.M.I., Zimmerman, A.S. Image processing using the PCNN time matrix as a selective filter[C]//Image Proceedings,2003. ICIP 2003. Proceedings.2003 International Conference on. IEEE.2003,1(1):Ⅰ-877-80.
[60]Qu, H., Yi, Z. A new algorithm for finding the shortest paths using PCNNs[J]. Chaos, Solitons & Fractals.2007,33(4):1220-1229.
[61]Wang, Z., Ma, Y, Gu, J. Multi-focus image fusion using PCNN[J]. Pattern Recognition.2010, 43(6):2003-2016.
[62]Lindblad, T., Kinser, J.M. Image processing using pulse-coupled neural networks[M]. Springer.2005.
[63]Shang, L., Zhang, Y. A class of binary images thinning using two PCNNs[J]. Neurocomputing.2007,70 (4-6):1096-1101.
[64]Gu, X.D., Cheng, C.Q., Yu, D.H. Noise-reducing of four-level image using PCNN and fuzzy algorithm[J]. Journal of Electronics and Information Technology.2003,25(12):1585.
[65]毕英伟,邱天爽.一种基于简化PCNN的自适应图像分割方法[J].电子学报,2005,33(4)：647-650.
[66]Berg, H., Olsson, R., Lindblad, T., Chilo, J. Automatic design of pulse coupled neurons for image segmentation[J]. Neurocomputing.2008,71(10-12):1980-1993.
[67]Wei, S., Hong, Q., Hou, M. Automatic image segmentation based on PCNN with adaptive threshold time constant[J]. Neurocomputing.2011,74(9):1485-1491.
[68]Weber, E.H., De pulsu, resorptione, auditu et tactu. annotationes anatomicae et physiologicae. Leipzig, Germany:C.F. Kohler,1834.
[69]Fechner, G.T., Elemente der pshchophysik. Leipzig, Germany:Breitkopf & Hartel,1860.
[70]Broussard, R.P., Rogers, S.K., Oxley, M.E., et al. Physiologically motivated image fusion for object detection using a pulse coupled neural network[J]. IEEE Transactions on Neural Networks.1999,10(3):554-563.
[71]Ranganath, H.S., Kuntimad G.J., Johnson, L. Pulse coupled neural networks for image processing[J]. IEEE Southeastcon, Raleigh, NC.1995,37-43.
[72]Ranganath, H.S., Kuntimad, G. Object detection using pulse coupled neural networks[J]. IEEE Transactions on Neural Networks.1999,10(3):615-620.
[73]顾晓东;郭仕德;余道衡.一种用PCNN进行图像边缘检测的新方法.计算机工程与应 用,2003.39(16)：1-2,55.
[74]Kang Chungchia, Wang Wenjune. A novel edge detection method based on the maximizing objective function[J]. Pattern Recognition.2007,40(2):609-618.
[75]Zhang, J., Lu, Z., Shi, L., et al. Filtering images contaminated with pep and salt type noise with pulse-coupled neural networks[J]. Science in China Series F:Information Sciences. 2005,48(3):322-334.
[76]Wang, Z.., Ma, Y., Xu, G. A novel method of iris feature extraction based on the ICM[C]. Proc. of the International Conference on Information Acquisition.2006,814-818.
[77]Bouzouba, K., Radouane, L. Image identification and estimation using the maximum entropy principle[J]. Pattern Recognition Letters.2000,21(8):691-700.
[78]Ma, Y., Wang, Zhaobin, Wu, C. Feature extraction from noisy image using PCNN[C]. Proc. of the International Conference on Information Acquisition.2006,808-813.
[79]Ma, Y., Lin, D., Zhang, B., et al. A novel algorithm of image enhancement based on pulse coupled neural network time matrix and rough set[C]. Fuzzy Systems and Knowledge Discovery,2007. FSKD 2007. Fourth International Conference on. IEEE.2007,3:86-90.
[80]Vega-pineda, J., Chacon-Murguia, M.I., Camarillo-Cisneros, R. Synthesis of pulse-coupled neural networks in FPGAs for real-time image segmentation[C]. Proc. of International Joint Conference on Neural Networks.2006,4051-4055.
[81]Kinser, J.M., Lindblad, T. Implementation of pulse-coupled neural networks in a CNAPS environment[J]. Neural Networks, IEEE Transactions on.1999,10(3):584-590.
[82]Forgac, R., Mokris, I. Feature generation improving by optimized PCNN[C]. Proc. Of 6th International Symposium on Applied Machine Intelligence and Informatics.2008,203-207.
[83]Johnson, J.L. Pulse-coupled neural nets:translation, rotation, scale and intensity signal invariances for image [J]. Applied Optics.1994,33(26):6239-6253.
[84]Yide, M., Qing, L., Zhibai, Q. Automated image segmentation using improved PCNN model based on cross-entropy[C]. Intelligent Multimedia, Video and Speech Processing,2004. Proceedings of 2004 International Symposium on. IEEE.2004:743-746.
[85]章毓晋.图像分割[M].科学出版社.2001.
[86]Otsu, N. A threshold selection method from gray-level histograms[J]. Automatica.1975, 11(285-296):23-27.
[87]Felzenszwalb, P.F., Huttenlocher, D.P. Efficient graph-based image segmentation[J]. International Journal of Computer Vision.2004,59(2):167-181.
[88]Zhang, Y.J. A review of recent evaluation methods for image segmentation[C]. Signal Processing and its Applications, Sixth International, Symposium on.2001. IEEE.2001,1: 148-151.
[89]马义德,钱志柏.基于聚类算法的图像分割技术[J].中国科技论文在线,2004,03,18.
[90]钱志柏.基于模糊聚类和PCNN的图像分割新算法研究[硕士论文].兰州：兰州大学.2004.
[91]Mario, F., Giuseppe, B., Terry, C. Entropy-based representation of image information[J]. Pattern Recognition Letters.2002,23(12):1391-1398.
[92]Kanungo, T., Mount, D.M., et al. An efficient k-means clustering algorithm:analysis and implementation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002, 24(7):881-892.
[93]Wu, H.S., Barba, J., Gil, J. A parametric fitting algorithm for segmentation of cell images[J]. IEEE Transactions on Biomedical Engineering.1998,45(3):400-407.
[94]黄凤岗,杨国,宋克鸥.柔性(soft)形态学在图像边缘检测中的应用[J].中国图象图形学报,2000,5(4)：284-287.
[95]杨文杰,刘浩学,马昆.边界探测的小波变换方法[J].中国图象图形学报.1999,4(1)：38-40.
[96]王浩军,毛柏鑫,笃彦等.原位分子杂交图像中银粒的分割[J].中国图象图形报.1999,4(6)：454-457.
[97]耿伯英,杨静宇.一种基于一致性邻域超图模型的图像分割[J].中国图象图形学报,2000,5(4)：288-292.
[98]魏志成,周激流,吕航等.一种新的图像分割自适应算法的研究[J].中国图象图形学报.2000,5(3)：217-220.
[99]Kurugollu, F., Sankur, B., Emre Harmanci A. Image segmentation by relaxation using constraint satisfaction neural network[J]. Image and Vision Computing.2002,20(7): 483-497.
[100]Chang, C.L., Ching, Y.T. Fuzzy Hopfield neural network with fixed weight for medical image segmentation[J]. Optical Engineering.2002,41(2):351-358.
[101]Skourikhine, A.N. Pulse couple neural network for image smoothing and Segmentation[A]. International Symposium on Computational Intelligence[C]. Kosice, Slovakia,2000.
[102]Ma Yide, Dai Rolan, Li Lian, et al. Image segmentation of embryonic plant cell using pulse-coupled neural networks[J]. Chinese Science Bulletion.2002,47(02):167-172.
[103]刘勃,马义德.一种基于交叉熵改进型PCNN图像自动分割新方法[J].中国图象图形学报.2005,10(5)：579-584.
[104]Spreeuwers, L.J. Neural network edge detector[C]. Electronic Imaging'91, San Jose, CA. International Society for Optics and Photonics.1991:204-215.
[105]Dhawan, A.P., Dufresene, T. Low-level image processing and edge enhancement using a self-organizing neural network[J]. Proc.IEEE J Conf.on Neural networks.1990:503-510.
[106]邓翔宇,马义德.PCNN参数自适应设定及其模型的改进[J].电子学报.2012,40(5)：955-964.
[107]Ranganath, H. S., Kuntimad, G. Object detection using pulse coupled neural networks [J]. IEEE Transactions on Neural Networks.1999,10(3):615-620.
[108]Gu Xiaodong, Wang Yuanyuan, Zhang Liming. Object detection using unit-linking PCNN image icons [J]. Lecture Notes in Computer Science.2006,3972:616-622.
[109]Yu, B., Zhang, L.. Pulse coupled neural network for motion detection[C]. Proc. of the Joint International Conferences on Neural Networks.2003,1179-1184.
[110]Ekblad, U., Kinser, J.M. Theoretical foundation of the intersecting cortical model and its use for change detection of aircraft, cars, and nuclear explosion tests[J]. Signal Processing.2004, 84(7):1131-1146.
[111]Fabio, Pacifici., Fabio Del Frate. Automatic change detection in very high resolutionlmages with pulse-coupled neural networks[J]. IEEE Geoscience and Remote Sensing Letters.2010, 7(1):58-62.
[112]Hongzhao Y., Guifa H., Yong L. Pulse Coupled Neural Network Algorithm for Object Detection in Infrared Image[C]. Computer Network and Multimedia Technology.2009, CNMT 2009. International Symposium on. IEEE,2009:1-4.
[113]宋寅卯,袁端磊,卢易枫等.基于最优PCNN模型的织物疵点白动检测[J].仪器仪表学报,2008,29(4)：888-891.
[114]刘勃,许录平,马义德等.结合灰度嫡变换的PCNN小目标图像检测新方法[J].北京理工大学学报.2009,29(12)：1085-1090.
[115]Chen Qiuhong, Zhou Liang. A pulse-coupled neural network for color image edge detection[C]. Proceedings of the 8th WSEAS International Conference on Applied Computer and Applied Computational Science.2009,441-445.
[116]Bellon, O., Silva, L. New improvements to range image segmentation by edge detection. IEEE Signal Process Letters.2002,9 (2):43-45.
[117]Arbelaez, P., Maire, M., Fowlkes, C. et al. Contour detection and hierarchical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence.2010,33(5): 898-916.
[118]Spacek, A.. Edge detection and motion detection. Image and vision computing.1986,4(1): 43-56.
[119]Yongsheng Gao, M. K. H. Leung. Face recognition using line edge map. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002,24(6):764-79.
[120]Qiuying Yang., Xingyuan Gao. Tracking on motion of small target based on edge detection. In:Proceedings of 2009 WRI World Congress on Computer Science and Information Engineering, Los Angeles, CA, USA.2009,6:619-622.
[121]史飞.脉冲耦合神经网络在图像处理中的应用研究[硕士论文].兰州：兰州大学.2003.
[122]马义德,张祥光.非线性滤波器除噪技术综述[J].中国科技论文在线.2004.
[123]张兆礼,赵春晖,梅晓丹.现代图像处理技术及MATLAB实现[M].北京：人民邮电出版社.2001.
[124]Brownrigg, D.R.K. The weighted median filter[J]. Communications of the ACM.1984, 27(8):807-818.
[125]阮秋琦.数字图像处理学[M].北京：电子工业出版社.2001.
[126]Ko, S.J., Lee, Y.H. Center weighted median filger and their application to image enhancement[J]. IEEE Trans. On Circ. Syst.1991,38:984-993.
[127]梁雯,刘松林.图像中心加权中值滤波的改进与应用[J].中国图象图形学报.1997,2(8,9)：629-632.
[128]冯星奎,肖兴明,尹洪君.方向加权中值滤波算法[J].中国图象图形学报.2000,5(7)：609-611.
[129]Sun, T., Neuvo, Y. Detail-preserving median based filters in image processing[J]. Pattern Recognition Letters.1994,15(4):341-347.
[130]Yang Ruikang. Optimal weighted median filtering under structural constrains[J]. IEEE Transactions on Signal Processing.1995,43(3):591-603.
[131]常瑞娜,穆晓敏,杨守义等.基于局部空间像素特征的白适应加权滤波算法[J].计算机工程与应用.2008,44(6)：45-47.
[132]Eng, H.L., Ma, K.K. Noise adaptive soft-switching median filter[J]. Image Processing, IEEE Transactions on.2001,10(2):242-251.
[133]Brownrigg, D. Decision-based median filter using local signal statistics[C]. Proc.SPIE IntSymp. Visual Communications Image Processing, chicago.1994,2308:268-275.
[134]黄煦涛.二维数字信号处理Ⅱ-变换与中值滤波器[M].北京：科学出版社.1985.
[135]Czerwinski, R.N., Jones, D.L., Brien, W.D. Ultrasound speckle reduction by directional median filtering[A]. Proc.IEEE Int. Conf.Image Processing,Wasington DC, USA.1995, 358-361.
[136]齐春亮,马义德.自适应中值滤波器的实现与在图像降噪中的应用.中国科技论文在线2005,03,15.
[137]蔡汉添.小波变换域中图像噪声平滑技术[J].光学技术,1998,6：6-9.
[138]Donoho, D.L. De-noising by soft-thresholding[J]. IEEE Trans.Inform. Theory.1995,41(3): 613-627.
[139]张久文,马义德.一种基于小波变换的迭代自适应图像除噪算法[J].兰州大学学报.2005,41(2)：74-77.
[140]Sternberg, S.R. Grayscale morphology[J]. Computer Vision,Graphics,and Image Processing. 1986,35(1):333-355.
[141]Sinha, D., Dougherty, E.R. Fuzzy mathematical morphology [J]. Journal of Visual Communication and Image Representation.1992, (3):286-302.
[142]Koskinen, L., Astola J., Neuvo, Y. Soft morphological filters[C]. Proc.SPIE Int.Society of Optical Engineering.1991,1568:262-270.
[143]刘志敏,杨杰.基于数字形态学的图像形态滤波[J].红外与激光工程.1999,28(4)：10-15.
[144]马义德,张祥光,杨淼.基于多结构元广义形态滤波的改进算法[J].电子科技大学学报.2004,33(4)：391-394.
[145]马义德,杨淼,李廉.一种全方位多角度自适应形态滤波器及其算法[J].通信学报.2004,25(9)：86-92.
[146]Yuksel, M.E. A hybrid neuro-fuzzy filter for edge preserving restoration of images corrupted by impulse noise[J]. Image Processing, IEEE Transactions on.2006,15(4):928-936.
[147]Morillas, S., Gregori, V, Peris-Fajarnes, G., et al. Local self-adaptive fuzzy filter for impulsive noise removal in color images[J]. Signal Processing.2008,88(2):390-398.
[148]Chenchen Liu, Zhimeng Zhang. Sonar images de-noising based on pulse coupled neural networks[C].1st International Congress on Image and Signal Processing.2008,403-406.
[149]Yi-de M., Fei, S., Lian, L. Gaussian noise filter based on PCNN[C]. Neural Networks and Signal Processing,2003. Proceedings of the 2003 International Conference on. IEEE.2003, 1:149-151.
[150]Yide Ma, dongmei Lin, Beidou Zhang, et al. A novel algorithm of image Gaussian noise filtering based on PCNN time matrix[C].2007 IEEE international Conference on Signal processing and Communications.2007,1499-1502.
[151]石美红,毛江辉,梁颖等.一种强高斯噪声的图像滤波方法[J].计算机应用.2007,27(7)：1637-1640.
[152]Yongqiu Tu,Shaofa Li, Minqin Wang. Mixed-noise removal for color images using modified PCNN model[C]. Second International Symposium on Intelligent Information Technology Application.2008,347-351.
[153]Zou, B., Zhou, H., Chen, H, et al. Multi-Channel Image Noise Filter based on PCNN[J]. Journal of Computers.2012,7(2):475-482.
[154]Jinping He, Kun Gao, Guoqiang Ni. A novel method of image Gaussian noise filtering based on series connected PCNN model[C].2008 International Conference on Optical instruments and Technology:Optical Systems and Optoelectronic Instruments.2008,16-19.
[155]He, K., Li, S.F, Wang, C. Modified PCNN model and Its application to mixed-noise Removal[C]. Innovative Computing & Communication,2010 Intl Conf on and Information Technology & Ocean Engineering,2010 Asia-Pacific Conf on (CICC-ITOE). IEEE.2010: 213-216.